In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4} or Coxeter symbol qδ4 representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group D ~ n − 1 {\displaystyle {\tilde {D}}_{n-1}} for n ≥ 5, with D ~ 4 {\displaystyle {\tilde {D}}_{4}} = A ~ 4 {\displaystyle {\tilde {A}}_{4}} and for quarter n-cubic honeycombs D ~ 5 {\displaystyle {\tilde {D}}_{5}} = B ~ 5 {\displaystyle {\tilde {B}}_{5}} .